Infinitely Many Solutions for a Superlinear Fractional p‐Kirchhoff‐Type Problem without the (AR) Condition

Xiangsheng Ren, Jiabin Zuo, Zhenhua Qiao and Lisa Zhu

Advances in Mathematical Physics, 2019, vol. 2019, issue 1

Abstract: In this paper, we investigate the existence of infinitely many solutions to a fractional p‐Kirchhoff‐type problem satisfying superlinearity with homogeneous Dirichlet boundary conditions as follows: [a+b(∫R2Nux-uypKx-ydxdy)]Lpsu-λ|u|p-2u=gx,u, in Ω, u=0, in RN∖Ω, where Lps is a nonlocal integrodifferential operator with a singular kernel K. We only consider the non‐Ambrosetti‐Rabinowitz condition to prove our results by using the symmetric mountain pass theorem.

Date: 2019
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https://doi.org/10.1155/2019/1353961

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Persistent link: https://EconPapers.repec.org/RePEc:wly:jnlamp:v:2019:y:2019:i:1:n:1353961

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